Abstract
We study the stability of particles in slip-stacking configuration, used to nearly double proton beam intensity at Fermilab. We introduce universal area factors to calculate the available phase space area for any set of beam parameters without individual simulation. We find perturbative solutions for stable particle trajectories. We establish Booster beam quality requirements to achieve 97\% slip-stacking efficiency. We show that slip-stacking dynamics directly correspond to the driven pendulum and to the system of two standing-wave traps moving with respect to each other.
Highlights
Slip stacking is integral to the high-intensity operation at Fermilab and will likely play a central role in upgrades to the accelerator complex [1,2,3]
We show that slip-stacking dynamics directly correspond to the driven pendulum and to the system of two standing-wave traps moving with respect to each other
We introduce the quasisynchronous particle trajectory and provide a perturbative solution near it
Summary
Slip stacking is integral to the high-intensity operation at Fermilab and will likely play a central role in upgrades to the accelerator complex [1,2,3]. Single-particle dynamics associated with slip-stacking contribute directly to the particle losses. This paper analyzes these dynamics at depth, both analytically and numerically. Our numerical results completely characterize the stable phase-space boundary We use these results to recommend an upgrade to the Fermilab Booster that would substantially reduce slip-stacking losses. Our analytical results provide insight into slip stacking by presenting a perturbative general solution and new parameteric resonances. These results should be of interest to the greater field of dynamical mathematics because, as we demonstrate, the dynamics of slip stacking are isomorphic to the well-studied dynamics of the driven pendulum. The analysis in this paper is intended to facilitate application of slip stacking to other accelerators and nonaccelerator systems with analogous dynamics
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